We prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, once localized at the quantum parameter, has a non trivial involution mapping Schubert classes to multiples of Schubert classes. This can be stated as a strange duality property for the Gromov-Witten invariants, which turn out to be very symmetric.

Following V.I. Arnolds techniques, we construct a local canonical form called miniversal deformation, for a family of differentiable regularizable linear dynamical systems Eẋ(t) = Ax(t)+Bu(t) under feedback and derivative feedback equivalence. We show some applications to the analysis of perturbations of a given regularizable system. c © 2008 Elsevier Ltd. All rights reserved.

I review some recent developments in the study of quark flavor distributions in the nucleon, including (i) valence quark distributions and the quark–hadron duality prediction for the x → 1 d/u ratio (ii) sea quark asymmetries and electromagnetic form factors (iii) strange quarks in the nucleon.

We consider moduli spaces of semistable sheaves on an elliptically fibered K3 surface, so that the first Chern class of the sheaves is a numerical section. For pairs of complementary such moduli spaces subject to numerical restrictions, we establish the strange duality isomorphism on sections of theta line bundles.

We determine the splitting type of the Verlinde vector bundles in higher genus in terms of simple semihomogeneous factors. In agreement with strange duality, the simple factors are interchanged by the Fourier-Mukai transform, and their spaces of sections are naturally dual.

The Poincaré series pA(t) of the coordinate algebra A of a normal surface singularity (X,x) with good C∗-action is written in a certain way as a quotient of two polynomials φA(t)/ψA(t). For a Kleinian singularity, we derive from the McKay correspondence that φA(t) and ψA(t) are the characteristic polynomials of the Coxeter element and the affine Coxeter element respectively. We show that if (X,...

We consider electric-magnetic duality(S-duality) in IIB matrix model with a D3-brane background. We propose the duality transformation by considering that of noncommutative Yang-Mills theory(NCYM) in four dimension. NCYM derived from the matrix model has a Yang-Mills coupling related to the noncommutativity of the spacetime. We argue that open strings bits as bi-local fields on the spacetime ar...

The goal of this document is to give a non-technical and imprecise introduction to the strange duality conjecture for surfaces. On the way, we will spend time on Chern classes and moduli of coherent sheaves. Throughout, S will be a smooth projective surface over C and KS will denote a canonical divisor on S. All of the general concepts, such as Chern classes, make sense for varieties of other d...